Question

If 2 x = 4 y = 8 z and 1 2x + 1 4y + 1 8z = 44 7 Show that x = 7 32 , y = 7 64 , z = 7 96

Answer 1







Giventhat2x=4y=8z−−(1)and,xyz=288−−−(2)usingequn(1)weget2x=(22)y=(23)z⇒2x=22y=23z[∴(am)n=amn]⇒x=2y=3z⇒x=2yandx=3z⇒x=2yandx=3z∴y=2xandz=3xNow,subsitute(y=2x)&(z=3x)inequn(2)Wehavex(2x)(3x)=288⇒x3=288×6⇒x3=1728∴x=12∴y=612=6&z=312=4∴2x1+4y1+8z1=2×121+4×61+8×41=241+241+321=9611Hence,optionBiscorrect.